The fate of singularities in quantum cosmology and the application of generalized effective equations to constrained quantum systems

Abstract

The first part of the thesis is concerned with the fate of singularities in quantum cosmology. The second part addresses the derivation of predictions from quantum cosmology. In the first part, two classes of cosmological models were studied. In the first class of models, the universe evolves to or emerges from a big-rip singularity. Here, energy density, pressure and scale factor diverge after a finite amount of time. This type of singularity arises rather generically in cosmological models with phantom dark energy. For each of these phantom-field models, the corresponding scenario with ordinary scalar field was studied. The scalar field induced a big-bang singularity. The second class of models studied was dominated by a big-brake singularity. At the big brake, the universe evolution comes to a halt due to an infinite deceleration. The motivation behind this choice of models was the occurrence of a singularity at large scale factor. The major question pursued was whether these types of singularity were resolved on the quantum level. If such singularities were resolved in quantum cosmology, this would imply that quantum gravitational effects can occur in the macroscopic universe. After devising classical models that contain the respective singularity, I subjected these models to quantization which was carried out in the geometrodynamical approach. The governing equation is then the WheelerDeWitt equation ...

Zsfassung in dt. und engl. Sprache